Journal of the Royal Statistical Society Series B (Statistical Methodology)

Smith, Cedric A. B.

doi: 10.1111/j.2517-6161.1953.tb00133.xpmid: N/A

There are three methods used in practice to detect human linkage. These are: (i) The sib‐pair method of Penrose, applicable to pairs of brothers and sisters, when the parents' genotypes are unknown or disregarded. (ii) The method of efficient scores (u‐functions), due to Fisher and Finney, applicable to families consisting of 2 or more children, together with either or both genotypes of the parents if known. (iii) The method of likelihood ratio, or backward odds, due to Haldane & Smith, and most suitable for large pedigrees: this links up with maximum likelihood estimation.

doi: 10.1111/j.2517-6161.1953.tb00134.xpmid: N/A

Hotelling, Harold

doi: 10.1111/j.2517-6161.1953.tb00135.xpmid: N/A

doi: 10.1111/j.2517-6161.1953.tb00136.xpmid: N/A

Kamat, A. R.

doi: 10.1111/j.2517-6161.1953.tb00137.xpmid: N/A

In the first part the property of “minimum error”, proved by Fisher for the estimates based on the powers of the deviations from the mean, is extended to the estimates based on the powers of the absolute values of variate differences. Efficiencies of certain of these statistics are also compared for small samples. In the second part the bias and the variance is evaluated when there is a “slow moving” trend in the mean. Finally in the third part a proof is given of a property possessed by the moments of certain ratio statistics derived from these estimates.

Moran, P. A. P.

doi: 10.1111/j.2517-6161.1953.tb00138.xpmid: N/A

In a previous paper the estimation of the sum λ + μ of the parameters of a simple birth and death process was considered. In the present paper we consider the estimation of λ(λ + μ)–1. This problem is equivalent to the problem of estimating the probabilities of steps to the right and left from an observed realization of a random walk which has one absorbing boundary and which is terminated, if necessary, after a preassigned number of steps. The properties of various estimators are considered.

Sundrum, R. M.

doi: 10.1111/j.2517-6161.1953.tb00139.xpmid: N/A

Pitman's formula for the variance of a distribution‐free test of two samples, due to Wilcoxon, is evaluated for some special cases. The upper bound of this variance is derived, and a population is constructed in which this upper bound is attained. The value of the variance is then used to find the power of the test against normal and rectangular alternatives for large samples and to compare this test with certain distributional tests.

Yates, F.; Grundy, P. M.

doi: 10.1111/j.2517-6161.1953.tb00140.xpmid: N/A

In selection with probability proportional to size x from within strata without replacement, the usual method of selection gives rise to bias in the estimate of the total of a variate y derived by weighting the units by weights proportional to 1/x. By means of numerical examples it is shown that the amount of this bias is usually quite trivial. If, however, unbiased estimates are required, the true total probabilities of selection of the different units can be calculated easily for samples of 2, and with considerably more labour for samples of 3.

Durbin, J.

doi: 10.1111/j.2517-6161.1953.tb00141.xpmid: N/A

The main purpose of the present paper is to give a rule for calculating estimates of sampling error which can be applied to multi‐stage designs of any degree of complexity. The rule is an extension of that given by Yates (1949) for the case of equal probabilities of selection. The paper goes on to discuss the relation between the theories of sampling with and without replacement and two approximate procedures are described which are easy to apply but lead to slight overestimates of sampling error.

doi: 10.1111/j.2517-6161.1953.tb00142.xpmid: N/A